Abstract

In this paper, we introduce a new class of monotone operators ? (H(·, ·), ?)- monotone operators, which generalize manyexisting monotone operators. The resolvent operator associated with an (H(·, ·), ?)- monotone operator is defined andits Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusioninvolving (H(·, ·), ?)-monotone operators and construct a new algorithm for solving the generalized mixed variational inclusion.Under some suitable conditions, we prove the convergence of the iterative sequences generated by the algorithm.These results improve and generalize many corresponding results in recently literatures.

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